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Lateral and consolidation behaviors of seabed-type breakwater for very soft ground
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Ocean Engineering 34 (2007) 2240–2250 www.elsevier.com/locate/oceaneng
Lateral and consolidation behaviors of seabed-type breakwater for very soft ground In Sung Jang, O Soon Kwon, Woo Sun Park, Weon Mu Jeong Harbor and Coastal Zone Development Research Division, Korea Ocean Research & Development Institute, 1270, Sa-dong, Ansan-si, Gyeonggi-do 425-170, Republic of Korea Received 3 December 2006; accepted 4 June 2007 Available online 3 July 2007
Abstract A seabed-type of breakwater applicable to very soft ground without the need for soil improvement is newly developed. This type of soft-ground breakwater is expected to ensure sufficient lateral resistance and prevent excessive consolidation settlement due to self-weight of the breakwater. In this paper, lateral and consolidation behaviors of soft-ground breakwater were investigated by performing model tests and finite element simulations. The results revealed that the bottom wall and buoyant box, which are the main features of softground breakwater, contribute to the increase in lateral resistance and to the control of the consolidation settlements, respectively, and that Terzaghi’s consolidation theory could be conservatively adopted in deriving the consolidation settlements of soft-ground breakwater proposed herein. r 2007 Elsevier Ltd. All rights reserved. Keywords: Soft-ground breakwater; Model tests; Finite element simulations; Bottom wall; Buoyant box; Lateral resistance; Consolidation settlements; Terzaghi’s consolidation theory
1. Introduction Before breakwaters are constructed on a very soft ground such as normally consolidated clayey soils and loose sandy soils, the ground must be improved with considerable cost and time. Conventional breakwaters such as a rubble mound breakwater and a caisson breakwater constructed on soft ground has revealed several problems: low economical efficiency, construction difficulty, safety concerns and seawater pollution due to heavy dredging and dumping materials. Many attempts have been made to develop new types of breakwaters that can be efficiently applied to soft ground, for example, a floating-type breakwater, a membrane-type breakwater, a pile-type breakwater, a curtain-type breakwater and so on (Giles and Sorensen, 1979; Hales, 1981; Markle and Cialone, 1987; Cho and Kim, 1998). These breakwaters can be applied to soft ground, however, not as
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E-mail address: [email protected] (I.S. Jang). 0029-8018/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2007.06.003
the main breakwater, but as the secondary assistant breakwater. The authors have developed a new seabed-type of breakwater applicable to very soft ground (called softground breakwater), as shown in Fig. 1, which can overcome the problems of conventional breakwaters indicated above (Park et al., 2002). The construction of the seabed-type breakwater on very soft ground should consider two requirements: the prevention of excessive consolidation settlement due to the self-weight of the structure, and the assurance of sufficient lateral resistance against wave actions. The soft-ground breakwater developed herein is expected to satisfy the above two requirements, because it uses a buoyant box and a bottom wall, which are two distinctive features that make the newly developed breakwater different from the previous seabedtype breakwater constructed at Kumamoto port in Japan (Monji et al., 1989). In this paper, the lateral behavior against wave loading and consolidation behavior due to self-weight of the softground breakwater were evaluated by performing model tests and numerical simulations. The effects of various
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Fig. 1. Basic concept of the soft ground breakwater.
factors such as the dimensions of the soft-ground breakwater and soil conditions on the lateral and consolidation behaviors were also examined. Furthermore, the applicability of the Terzaghi’s one-dimensional (1-D) consolidation theory, which has generally and practically been used as an evaluation method of consolidation settlements to the soft-ground breakwater, was also investigated. 2. Resistance mechanism of soft-ground breakwater In a conventional caisson-type breakwater, the friction between riprap and concrete is a crucial resistance against the lateral wave force (F), as shown in Fig. 2a. In a softground breakwater proposed herein, on the other hand, the friction between the ground and the structure is very small because of the minimized self-weight of the breakwater. The proposed breakwater has structural stability against lateral loading because of its three main resistances (Fig. 2b): the passive Earth pressure force (Fp) acting on both sides of the bottom wall and the embedded wall stem, the cohesion force (Fc) along the failure line connecting the ends of the bottom walls, and the vertical reaction force of the ground (FR). In the previous seabed-type of breakwater used at Kumamoto Port in Japan, a conventional pile foundation system was used to resist lateral loading, and the breakwater could not be used for very soft ground because of its high self-weight. 3. Terzaghi’s 1-D consolidation theory The consolidation settlements of clayey soils are generally computed by using Eq. (1) based on the 1-D consolidation theory of Terzaghi (1943). However, there may be some errors in applying Terzaghi’s theory for real conditions, which actually involve 2-D or 3-D problems. Skempton and Bjerrum (1957) have considered the 3-D effect by modifying the 1-D consolidation settlements with a correction factor (m), as shown in Eq. (2): 0 Cc s þ Ds0v Sc ¼ log v0 0 , (1) 1 þ e0 sv0 where Sc is the consolidation settlement, Cc is the compression index, e0 is the initial void ratio, s0 v0 is the
Fig. 2. Resistance mechanism against lateral wave actions: (a) conventional breakwater; and (b) soft ground breakwater.
initial stress, and Ds0 v is the stress increment. SA c ¼ mS c ,
(2)
where SA c is the consolidation settlement considering the three-dimensional effect, and m is a function of Skempton’s pore pressure coefficient (A), and the geometry of the problem. Most studies on consolidation settlement of a conventional breakwater used on soft ground have alternatively focused on finite element plane strain analysis (Brugger et al., 1998). For practical use, however, the 1-D consolidation theory has generally been used to calculate consolidation settlement, because numerical analyses are difficult to adopt in designing breakwaters. From the 1-D consolidation theory, consolidation settlements have been evaluated using data on stress increment in soil mass due to the self-weight of breakwaters. On the other hand, the 1-D consolidation theory could not be directly applied to the soft-ground breakwater because the actual consolidation behavior of the breakwaters with bottom walls is somewhat different from that predicted by theory. The difference may be caused by the increase in the resistance due to the bottom walls, and by the concentration of the stress increment (generated by loading) at the bottom wall. For a piled raft, whose system is similar to the understructure of the soft-ground breakwater, the consolidation settlement is generally calculated
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Fig. 4. Soil test tank.
Fig. 3. Location of the equivalent footing in the evaluation of settlement of the piled raft.
under the assumption that the clay between the tops and the lower third points of the piles is incompressible and that the load is applied to the soil at the lower third points of the piles, as shown in Fig. 3 (Duncan and Buchignani, 1976). However, it is necessary to examine the consolidation behavior of the soft-ground breakwater and the applicability of 1-D consolidation theory to the breakwater, because the breakwater proposed herein has a more complex understructure system than a piled raft.
4. Model test and numerical simulations 4.1. Model test set-up Both lateral load tests and consolidation model tests were carried out with the soil test tank as shown in Fig. 4. The size of the test tank is 0.3 m(width) 0.6 m (height) 7.2 m(length). Both sides were made of glasses 0.01 m thick, and drainage was permitted in both top and bottom directions. The clay layers for both lateral and consolidation tests were prepared in two steps. First, 0.05 m of Joomoonjin sand (Kim et al., 2005), which is generally used as standard sand in Korea, was underlain with filter papers, and then 0.5 m slurry layers were consolidated with self-weight for about 10days to stabilize the slurry. Second, additional upper clay layers were consolidated in the same pattern as that of the first step. The loading plate was laid on the filter paper at the ground surface. Several small mortar blocks were used as dead load only, to consolidate the kaolinite in slurry state. The total thicknesses of the clay layer were 0.4–0.45 m. The index properties of kaolinite used in the lateral load test are presented in Table 1.
Since it is difficult to prepare a new clayey soil layer consistent with the previous condition, lateral load tests and consolidation tests were separately performed by installing breakwaters of various dimensions in the individual soil ground. The various conditions of breakwater sections for lateral load tests and consolidation tests are presented in Tables 2 and 3, respectively. In the model tests to investigate lateral behavior, the incremental dead load was applied in the lateral direction to the breakwater (Fig. 5a). The lateral displacement was measured for each loading step. In the model tests to examine consolidation behavior, the dead loads were applied to the top of each breakwater at every loading step (Fig. 5b). The consolidation settlement for each breakwater was obtained with time by using 0.3 m rulers, which were attached to both sides of the breakwater. The next loading step was carried out only after no additional settlement occurred. 4.2. Numerical simulations Numerical analyses were conducted to investigate the effects of various factors, such as thickness of the clayey layer, embedded depth, buoyant box as well as base width and bottom wall length, on the lateral and consolidation behaviors of a soft-ground breakwater. A general-purpose finite element program ABAQUS (Anonymous, 1998) was employed alongwith consideration of the real soil and structural conditions. The analysis of the breakwater was treated as a two-dimensional plane strain problem. Eightnoded quadrilateral elements were chosen, and nine Gaussian points were used for the construction of the stiffness matrices. Fig. 6 shows the typical finite element mesh used in this study. The number of nodes and elements were 1749 and 587, respectively. The widths and heights of soil layers were 12H (H: the height from surface to top of the breakwater) and 2.6H, respectively. Thus, the effect of the outer boundary could be neglected. The boundary
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Table 1 Soil properties of kaolinite used in this test Soil properties
Specific gravity (Gs)
Unit weight (g, kg/m3)
Initial void ratio (e0)
Liquid limit (LL)
Plastic limit (PL)
Compression index (Cc)
Swelling index (Cs)
Value
2.61
1670
1.21
46.3
22.0
0.275
0.027
Table 2 Summary of lateral model test program
Base width (Bl, m) Bottom wall length (Dl, m)
LT-1
LT-2
LT-3
LT-4
LT-5
LT-6
LT-7
LT-8
LT-9
0.1 0
0.1 0.05
0.1 0.1
0.1 0.15
0.2 0
0.2 0.05
0.2 0.1
0.2 0.15
0.4 0
Note: Embedded depth (De,l) and height from the ground surface to the top of breakwater (Hl) is 0.025 m and 0.05 m for all types, respectively.
Table 3 Summary of consolidation model test program
Base width (Bc, m) Bottom wall length (Dc, m)
CT-1
CT-2
CT-3
CT-4
CT-5
CT-6
0.12 0.035
0.16 0
0.16 0.035
0.16 0.055
0.16 0.075
0.2 0.035
Note: Embedded depth (De,c) and height from the ground surface to the top of breakwater (Hc) are 0 m and 0.08 m for all types, respectively.
condition for displacement is specified as shown in Fig. 6, and initial static pore water pressures were applied at the soil elements by considering the water depth of 6 m. Throughout this paper, a volumetric work-hardening soil model, the modified cam clay (MCC) model, was used. The MCC model is based on the critical state concepts (Schofield and Wroth, 1968) and is capable of predicting quantitatively many of the observed features of normally consolidated and lightly overconsolidated clays, and has been used in predicting real boundary value problems. The consolidation analysis was conducted by deploying Biot’s (1941) coupled consolidation theory. The breakwater was modeled as concrete beam elements, and a negative body force was applied for elements as buoyant force. Various conditions applied in the numerical simulations are presented in Table 4. For convenience, the dimensions of the breakwater were normalized by H. Table 5 shows the soil conditions used as input values in this analysis; they were classified into three types with respect to the consolidation characteristics: very soft clays (case I), soft clays (case II), and medium clays (case III). The values are based on the real soil conditions of the sites where port D is scheduled to be located in Korea (Park et al., 2002). For cases I and III in Table 5, the values of the other parameters including e0 were assumed to be the same as those of case II except l and k, which were varied only to determine the effect of the consolidation parameters on the consolidation behavior of the breakwater. For the simulation of lateral loading, the lateral displacement at the top of the breakwater was checked while the wave force was applied to the breakwater. The
period (T) and height (Hmax) of the wave were assumed to 3.5 s and 2.0 m, respectively. For the simulation of the consolidation process, the maximum consolidation settlements at the top of the breakwater were checked at the end of the consolidation process. 5. Lateral behavior of soft-ground breakwater The effects of the various factors such as dimensions of the structures and soil ground conditions on the lateral behavior of the breakwaters were investigated by model tests and numerical simulations. Fig. 7 shows the typical load-displacement curves for various conditions of breakwater, which were obtained from lateral model tests. The displacement was measured at a point 0.01 m below from the top of the breakwater. Test results in this study showed that regardless of the base width, the overturning failure mode was generally dominant over that of sliding, which may be due to the effect of breakwater embedment to the ground with values of 0.5Hl ( ¼ 0.025 m, Hl: the height from surface to the top of the breakwater in lateral model test), as indicated in Table 2. The effect of the embedded depth on the lateral behavior could be verified in Fig. 8, which compares the lateral displacements at the top of the breakwater for various embedded depths and thicknesses of the clayey layer. Unlike the model test results, numerical results in Fig. 8 were plotted in terms of the lateral displacement, which is also an important variable in designing breakwaters and is comparable to the maximum lateral resistance representing the maximum load corresponding to 0.0015 m of lateral displacement, as shown in
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I.S. Jang et al. / Ocean Engineering 34 (2007) 2240–2250 Table 4 Summary of numerical simulations Base width (B) Bottom wall length (D) Embedded depth (De) Thickness of soil layer (H’) Thickness of buoyant box (Hb)
1.5H, 2.0H, 2.5H, 3.0H, 3.75H 0H, 0.25H, 0.5H, 1.0H 0.0 m, 1.0 m, 2.0 m, 3.0m 1.0H, 1.5H, 2.0H, 2.5H, 3.0H 0.0 m, 0.25 m, 0.5 m, 0.75 m, 1.0 m
Note: The values in bold correspond to the elementary case in the parametric study.
Table 5 Input parameters used in finite element analysis Input parameters
g (kg/m3)
e0
l
k
f (1)
M
n0
K0
Case I Case II Case III
1500 1500 1500
1.0 1.0 1.0
0.52 0.37 0.13
0.058 0.040 0.002
25.4 25.4 25.4
1.0 1.0 1.0
0.3 0.3 0.3
0.5 0.5 0.5
Symbols) g : unit weight, e0 : initial void ratio, l(¼ Cc/2.3; Cc: compression index), k(¼ Cs/2.3; Ce: swelling index), f : internal friction angle, M : slope of critical state line, n0 : drained poisson’s ratio, K0 : earth pressure coefficient at rest.
Fig. 5. Basic concept of model test: (a) lateral test; and (b) consolidation test.
Fig. 7. Load–displacement curves for various breakwater sections (from model tests).
Fig. 6. Finite element mesh.
Fig. 7. Fig. 8 also reveals that the lateral displacement increases with increasing thickness of the clay layer, but is constant for a thickness higher than 2.0H. This means that
the soft-ground breakwater could be more effectively utilized for a site with a very thick clay layer than for conventional breakwaters. The effects of base widths and bottom wall lengths of soft-ground breakwaters on lateral behavior are shown in
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Fig. 9, which presents both the results of numerical simulations (Fig. 9a) and model tests (Fig. 9b). Both results reveal that the lateral displacement apparently decreases with the increase in base width and that the installation of the bottom wall has an effect on the lateral resistance as much as the increase in the base width. It is predicted that as the bottom wall length increases, the passive earth pressure force (Fp) acting on both sides of the bottom wall plays a great role in the resistance against overturning failure, rather than on the cohesion force (Fc) and on the vertical reaction force of the ground (FR). Therefore, if it is difficult to increase the base width because of economical and/or constructional problems, the lateral resistance can be successfully activated by installing the bottom wall.
Fig. 8. Comparison of lateral behavior for various embedded depths and thicknesses of clay layers (from numerical results).
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6. Consolidation behavior of soft-ground breakwater 6.1. Consolidation settlement with time and loads Consolidation model test results are shown in Fig. 10, which plot the load–settlement curves with time with respect to the base width and the bottom wall length. The curves are similar to the typical time-settlement curve measured at the base of embankment constructed on soft ground (Brugger et al., 1998). The consolidation settlements apparently increase with time as the bottom wall length and base width decreases. Fig. 11a shows the settlement due to applied loads in logarithm scale, for all fix types in the model test. The values at which no further increment occurred were plotted. The curves show that the abrupt settlements occurred at the second step (load ¼ 155.2 N) of CT-1, CT-2 and CT-3. For CT-1, the test was terminated because of the excessive punching shear failure in the second step of the consolidation process. The steep slopes in settlements may be related to the maximum past pressure, as also generally indicated by the conventional oedometer test results. However, it can be suggested that the steep slopes in this study are attributed to the effect of the instantaneous settlement due to applied load rather than the effect of the maximum past pressure because the kaolinite consolidated in slurry state, and the pressure due to mortar blocks as initial loads, which were applied at the ground surface prior to consolidation test, was less than 5 kPa. Instantaneous settlement generally means an elastic settlement. In this test, however, the elastic settlement calculated was less than 0.001 m, which can be negligible compared with total settlement. The results indicate that the settlement occurred in a plastic state rather than an elastic state, that is, at punching shear failure, which could be seen in a shallow foundation constructed on loose sands or sensitive clays. Therefore, the punching shear failure should be considered in the evaluation of the consolidation behaviors of the soft-ground breakwater.
Fig. 9. Comparison of lateral behavior for various base widths and bottom wall lengths: (a) numerical results; and (b) model test results.
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Fig. 10. Load–settlement curves with time (from model tests): (a) Loadsettlement curves for various base widths; (b) Load–settlement curves for various bottom wall lengths.
It is difficult to determine the pure consolidation settlement from the total settlement because instantaneous settlement due to the punching shearpffiffifailure cannot be obtained rigorously. In this study, the t method, which is one of the methods to estimate the coefficient of consolidation (cv) from a consolidation curve with time in a conventional oedometer test, was alternatively used to separate the instantaneous settlement from the total settlement. Fig. 12pshows the consolidation curve with ffiffi time plotted in the t axis, where the initial instantaneous settlement can be graphically evaluated by finding out the start time of consolidation (t0) from the initial tangential pffiffi line. The load–settlement curves modified by using the t method are shown in Fig. 11b.
Fig. 11. Settlements due to applied loads in logarithm scale for all six types: (a) original load–settlement curves; (b) modified load–settlement curves.
6.2. Parametric analysis on the consolidation settlement of the breakwater Consolidation settlement of the soft-ground breakwater is mainly influenced by the stress increment generated at soil mass due to self-weight of the breakwater. The effect of the stress increment was investigated by modeling numerically the consolidation of a soft-ground breakwater without a bottom wall. The variation of the vertical stress increment with depth was checked at the elements corresponding to the center of the base of the breakwater, which is plotted in Fig. 13. The stress increment decreases with the distance from the base, to be zero at about 20 m,
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Fig. 12. Consolidation curve with time plotted by the
pffiffi t method.
Fig. 13. Variation of the vertical stress increment with depth.
which is almost the same as a base width (B). The numerical results are somewhat different to the elastic solution of Boussinesq (1885), which shows 10% of the total load is transmitted up to the depth of 2B. This may be attributed to the fact that the stress increment at a soft soil
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with a plastic behavior is less than that of an elastic soil. This is why the stress increment for case III representing the relatively stiffer soil layer is transmitted to a higher depth than that for case I. It can also be predicted that the consolidation of the breakwater converges to a constant value if the thickness of the clayey layer is greater than twice the height of the breakwater. This is verified from Fig. 14a, which plots the maximum consolidation settlement with the thickness of the clay layer and the embedded depth. Numerical results in Fig. 14a also reveal that the consolidation settlement decreases as the embedded depth increases. This is because the adhesion of the clayey soils with a stem embedded into the ground contributes to restrain the consolidation settlement. One of the important features of the soft-ground breakwater is the buoyant box, which is utilized to reduce the self-weight of the breakwater. Finite element analyses were performed to examine the effect of the buoyant box on the consolidation settlement of the breakwater. As shown in Fig. 14b, which plots the maximum consolidation settlement with the thickness of the buoyant box for case II, the size of the buoyant box is linearly correlated to the consolidation settlement. As the thickness of the buoyant box increases, both the self-weight of the breakwater and the consolidation settlement decrease. The results indicate that the settlement can be effectively controlled with the buoyant box even for a very soft clay layer, where excessive settlement is predicted in a practical design. As the base width of the breakwater increases, the self-weight of the breakwater increases, but the stress increment decreases. Fig. 14c shows the numerical results of the maximum consolidation settlements with the base width (B) and the bottom wall length (D) of the breakwater for a ground condition of case II. The results for all cases show that the consolidation settlement decreases with increases in base width and bottom wall length. For a breakwater with a high bottom wall (D ¼ 1.0H), consolidation settlement is retarded by the bottom wall and not by the decrease in the stress increment, because the longer the bottom wall length the more a mobilized area to resist the settlement. In this case, the effect of the base width is of secondary importance. The settlement tendencies are almost the same, regardless of ground conditions. The model test results of the consolidation settlement with the base width and the bottom wall length are shown in Fig. 15. The results are modified in consideration of the pffiffi instantaneous settlement obtained by the t method, as mentioned above. The trend in the consolidation settlement with the bottom wall length and the base width is similar to the numerical results. From the numerical and model test results, it is suggested that the increase in the bottom wall length is more effective than the increase in the base width to reduce the consolidation settlement as well as the lateral resistance, if the economical design efficiency is considered.
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Fig. 15. Maximum consolidation settlements with the base width and the bottom wall length (model test results): (a) effect of the base width; and (b) effect of the bottom wall length.
7. Application of the Terzaghi’s one-dimensional consolidation theory
Fig. 14. Maximum consolidation settlements for various conditions (numerical results): (a) effect of embedded depth and thickness of clay layers; (b) effect of buoyant box; and (c) effect of base width and bottom wall length.
The consolidation settlements of the conventional breakwater have been generally computed by the Terzaghi’s 1-D consolidation theory. However, the soft-ground breakwater has a complex bottom wall system, so the theory cannot be applied directly. For convenience in practical design, the applicability of the Terzaghi’s theory to the soft-ground breakwater was examined by comparing the consolidation settlements obtained from numerical simulations and model tests with the computed values from the Terzaghi’s theory. The consolidation settlements of a breakwater without the bottom wall were obtained from numerical analysis and compared with theoretical values calculated with the stress increment at the mid-depth of single layer, as shown in Fig. 16, which reveals higher theoretical settlements than
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Fig. 16. Comparison of the settlements from the Terzaghi’s theory with FEM results.
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stress increments, which were checked at both the center and the edge of the base. The theoretical consolidation settlements modified by Skempton and Bjerrum (1957) were similar to the numerical results, which were between the values recalculated at the center and the edge. For a breakwater with a bottom wall, since the stress increment due to self-weight of the breakwater concentrates at the bottom wall, it is difficult to rigorously define the consolidation layer. Furthermore, the consolidation behavior may vary because of the increase in the resistance due to the installation of the bottom wall. To identify the relevant loading point in the application of the 1-D consolidation theory to the soft-ground breakwater, the numerical settlements were compared with the calculated ones, whose loading points were located at the tip of the bottom wall and the base, respectively (Fig. 18a). The 1-D consolidation settlements calculated under assumption that the load is applied to the soil at the tip were more similar to the numerical results than to the settlements obtained under the assumption that the base is the loading point. A similar trend can be verified from the model test results in Fig. 18b, which plots the comparison of the consolidation settlements from the model test with the calculated values. Fig. 18 indicates that the proposed evaluation method on the consolidation settlement of the soft-ground breakwater, based on the assumption of the tip of bottom wall as the loading point, can be used rather conservatively and easily with some accuracy. 8. Conclusions
Fig. 17. Comparison of the modified settlements with FEM results for case II.
the numerical settlements. The difference is caused by the fact that the numerical values are obtained under assumption of a 2-D plane strain condition and the plastic yield criterion, while the theoretical ones are calculated based on the 1-D elastic theory. To consider the 2-D effect, the consolidation settlement based on the Terzaghi’s theory was modified by using Eq. (2) of Skempton and Bjerrum (1957), as shown in Fig. 17. The correction factor, m ¼ 0.9 was obtained by assuming pore pressure parameter, A ¼ 0.75, which corresponds to normally consolidated clays. The effect of the stress increment was additionally investigated, as shown in Fig. 17, by recalculating the 1-D consolidation settlements using the numerical results of the
The authors developed a new seabed type of breakwater applicable to very soft ground, which is expected to satisfy two requirements: the prevention of excessive consolidation settlement due to the self-weight of the structure, and the assurance of sufficient lateral resistance against wave actions. From the results of model tests and numerical simulations performed to investigate the lateral and consolidation behaviors of the soft-ground breakwater, the following conclusions can be drawn. The soft-ground breakwater proposed herein can be used with high economic efficiency owing to its resistance mechanism, at a site with even a very thick clay layer. The base width and bottom wall length are mainly to do with lateral resistance, and if the base width is difficult to increase because of economical and/or constructional problems, the lateral resistance could be successfully assured by installing bottom walls. The consolidation settlement could be effectively controlled with the buoyant box even for a very soft clay layer, where excessive settlement is predicted in a practical design. The bottom wall can reduce the consolidation settlement efficiently because it can decrease the thickness of the consolidation layer and increase the resistance. Terzaghi’s one-dimensional consolidation theory can be adopted rather conservatively with some accuracy if the location
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Fig. 18. Comparison of the measured consolidation settlements with values from Terzaghi’s 1-D theory: (a) FEM results; and (b) model test results.
of consolidation loading is assumed to be at the end of the bottom wall. Acknowledgment This research was accomplished as a part of the project ‘‘Technologies for Breakwaters in Deep Water and Soft Ground Improvement’’, which was sponsored by Ministry of Maritime and Fishery in Korea. The authors express their appreciation for this support. References Anonymous, 1998. ABAQUS/Standard User’s Manual—Version 5.8. Hibbit, Kalsson and Sorenssen Inc. Biot, M.A., 1941. General theory of three-dimensional consolidation. Journal of Applied Physics 12, 155–164. Boussinesq, J., 1885. Application des Potentials a L’Etude de L’Equilibre et du Mouvement des Solides Elastiques. Gauthier-Villars, Paris. Brugger, P.J., Almeida, M.S.S., Sandroni, S.S., Lacerda, W.A., 1998. Numerical analysis of the breakwater construction of Segipe Harbour, Brazil. Canadian Geotechnical Journal 35, 1018–1031. Cho, I.H., Kim, M.H., 1998. Interactions of a horizontal flexible membrane with oblique waves. Journal of Fluid Mechanics 367, 139–161.
Duncan, J.M., Buchignani, A.L., 1976. An engineering manual for settlement studies. Geotechnical Engineering Report, Department of Civil Engineering, University of California at Berkeley, 94pp. Giles, M.L., Sorensen, R.M., 1979. Determination of mooring loads and transmission for a floating tire breakwater. In: Proceedings of the Coastal Structures 1979 Conference, vol II. ASCE, pp. 1069–1086. Hales, L.Z., 1981. Floating breakwaters : State-of-the-art literature review. US Army Coastal Engineering Research Center. CERC-TR-81-1. Kim, S.R., Jang, I.S., Chung, C.K., Kim, M.M., 2005. Evaluation of seismic displacements of quay walls. Soil Dynamics and Earthquake Engineering 25, 451–459. Markle, D.G., Cialone, M.A., 1987. Wave transmission characteristics of various floating and bottom-fixed rubber-tire breakwaters in shallow water. US Army Coastal Engineering Research Center, WES. Miscellaneous Paper CERC-87-8. Monji, T., Murayama, I., Motono, I., Takata, N., 1989. Development of moundless breakwater with wide footing on soft ground. Proceedings of Ocean Development 5, 103–107 (in Japanese). Park, W.S., Jang, I.S., Kwon, O.S., Yum, K.D., 2002. Development of a new type breakwater on very soft ground. Third Symposium on Northeast Asian Ports, pp. 82–93. Schofield, A.N., Wroth, C.P., 1968. Critical State Soil Mechanics. McGraw-Hill, New York. Skempton, A.W., Bjerrum, L., 1957. A contribution to the settlement analysis of foundations on clay. Geotechnique 7, 168–178. Terzaghi, K., 1943. Theoretical Soil Mechanics. Wiley, New York.
Ocean Engineering 34 (2007) 2240–2250 www.elsevier.com/locate/oceaneng
Lateral and consolidation behaviors of seabed-type breakwater for very soft ground In Sung Jang, O Soon Kwon, Woo Sun Park, Weon Mu Jeong Harbor and Coastal Zone Development Research Division, Korea Ocean Research & Development Institute, 1270, Sa-dong, Ansan-si, Gyeonggi-do 425-170, Republic of Korea Received 3 December 2006; accepted 4 June 2007 Available online 3 July 2007
Abstract A seabed-type of breakwater applicable to very soft ground without the need for soil improvement is newly developed. This type of soft-ground breakwater is expected to ensure sufficient lateral resistance and prevent excessive consolidation settlement due to self-weight of the breakwater. In this paper, lateral and consolidation behaviors of soft-ground breakwater were investigated by performing model tests and finite element simulations. The results revealed that the bottom wall and buoyant box, which are the main features of softground breakwater, contribute to the increase in lateral resistance and to the control of the consolidation settlements, respectively, and that Terzaghi’s consolidation theory could be conservatively adopted in deriving the consolidation settlements of soft-ground breakwater proposed herein. r 2007 Elsevier Ltd. All rights reserved. Keywords: Soft-ground breakwater; Model tests; Finite element simulations; Bottom wall; Buoyant box; Lateral resistance; Consolidation settlements; Terzaghi’s consolidation theory
1. Introduction Before breakwaters are constructed on a very soft ground such as normally consolidated clayey soils and loose sandy soils, the ground must be improved with considerable cost and time. Conventional breakwaters such as a rubble mound breakwater and a caisson breakwater constructed on soft ground has revealed several problems: low economical efficiency, construction difficulty, safety concerns and seawater pollution due to heavy dredging and dumping materials. Many attempts have been made to develop new types of breakwaters that can be efficiently applied to soft ground, for example, a floating-type breakwater, a membrane-type breakwater, a pile-type breakwater, a curtain-type breakwater and so on (Giles and Sorensen, 1979; Hales, 1981; Markle and Cialone, 1987; Cho and Kim, 1998). These breakwaters can be applied to soft ground, however, not as
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E-mail address: [email protected] (I.S. Jang). 0029-8018/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2007.06.003
the main breakwater, but as the secondary assistant breakwater. The authors have developed a new seabed-type of breakwater applicable to very soft ground (called softground breakwater), as shown in Fig. 1, which can overcome the problems of conventional breakwaters indicated above (Park et al., 2002). The construction of the seabed-type breakwater on very soft ground should consider two requirements: the prevention of excessive consolidation settlement due to the self-weight of the structure, and the assurance of sufficient lateral resistance against wave actions. The soft-ground breakwater developed herein is expected to satisfy the above two requirements, because it uses a buoyant box and a bottom wall, which are two distinctive features that make the newly developed breakwater different from the previous seabedtype breakwater constructed at Kumamoto port in Japan (Monji et al., 1989). In this paper, the lateral behavior against wave loading and consolidation behavior due to self-weight of the softground breakwater were evaluated by performing model tests and numerical simulations. The effects of various
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Fig. 1. Basic concept of the soft ground breakwater.
factors such as the dimensions of the soft-ground breakwater and soil conditions on the lateral and consolidation behaviors were also examined. Furthermore, the applicability of the Terzaghi’s one-dimensional (1-D) consolidation theory, which has generally and practically been used as an evaluation method of consolidation settlements to the soft-ground breakwater, was also investigated. 2. Resistance mechanism of soft-ground breakwater In a conventional caisson-type breakwater, the friction between riprap and concrete is a crucial resistance against the lateral wave force (F), as shown in Fig. 2a. In a softground breakwater proposed herein, on the other hand, the friction between the ground and the structure is very small because of the minimized self-weight of the breakwater. The proposed breakwater has structural stability against lateral loading because of its three main resistances (Fig. 2b): the passive Earth pressure force (Fp) acting on both sides of the bottom wall and the embedded wall stem, the cohesion force (Fc) along the failure line connecting the ends of the bottom walls, and the vertical reaction force of the ground (FR). In the previous seabed-type of breakwater used at Kumamoto Port in Japan, a conventional pile foundation system was used to resist lateral loading, and the breakwater could not be used for very soft ground because of its high self-weight. 3. Terzaghi’s 1-D consolidation theory The consolidation settlements of clayey soils are generally computed by using Eq. (1) based on the 1-D consolidation theory of Terzaghi (1943). However, there may be some errors in applying Terzaghi’s theory for real conditions, which actually involve 2-D or 3-D problems. Skempton and Bjerrum (1957) have considered the 3-D effect by modifying the 1-D consolidation settlements with a correction factor (m), as shown in Eq. (2): 0 Cc s þ Ds0v Sc ¼ log v0 0 , (1) 1 þ e0 sv0 where Sc is the consolidation settlement, Cc is the compression index, e0 is the initial void ratio, s0 v0 is the
Fig. 2. Resistance mechanism against lateral wave actions: (a) conventional breakwater; and (b) soft ground breakwater.
initial stress, and Ds0 v is the stress increment. SA c ¼ mS c ,
(2)
where SA c is the consolidation settlement considering the three-dimensional effect, and m is a function of Skempton’s pore pressure coefficient (A), and the geometry of the problem. Most studies on consolidation settlement of a conventional breakwater used on soft ground have alternatively focused on finite element plane strain analysis (Brugger et al., 1998). For practical use, however, the 1-D consolidation theory has generally been used to calculate consolidation settlement, because numerical analyses are difficult to adopt in designing breakwaters. From the 1-D consolidation theory, consolidation settlements have been evaluated using data on stress increment in soil mass due to the self-weight of breakwaters. On the other hand, the 1-D consolidation theory could not be directly applied to the soft-ground breakwater because the actual consolidation behavior of the breakwaters with bottom walls is somewhat different from that predicted by theory. The difference may be caused by the increase in the resistance due to the bottom walls, and by the concentration of the stress increment (generated by loading) at the bottom wall. For a piled raft, whose system is similar to the understructure of the soft-ground breakwater, the consolidation settlement is generally calculated
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Fig. 4. Soil test tank.
Fig. 3. Location of the equivalent footing in the evaluation of settlement of the piled raft.
under the assumption that the clay between the tops and the lower third points of the piles is incompressible and that the load is applied to the soil at the lower third points of the piles, as shown in Fig. 3 (Duncan and Buchignani, 1976). However, it is necessary to examine the consolidation behavior of the soft-ground breakwater and the applicability of 1-D consolidation theory to the breakwater, because the breakwater proposed herein has a more complex understructure system than a piled raft.
4. Model test and numerical simulations 4.1. Model test set-up Both lateral load tests and consolidation model tests were carried out with the soil test tank as shown in Fig. 4. The size of the test tank is 0.3 m(width) 0.6 m (height) 7.2 m(length). Both sides were made of glasses 0.01 m thick, and drainage was permitted in both top and bottom directions. The clay layers for both lateral and consolidation tests were prepared in two steps. First, 0.05 m of Joomoonjin sand (Kim et al., 2005), which is generally used as standard sand in Korea, was underlain with filter papers, and then 0.5 m slurry layers were consolidated with self-weight for about 10days to stabilize the slurry. Second, additional upper clay layers were consolidated in the same pattern as that of the first step. The loading plate was laid on the filter paper at the ground surface. Several small mortar blocks were used as dead load only, to consolidate the kaolinite in slurry state. The total thicknesses of the clay layer were 0.4–0.45 m. The index properties of kaolinite used in the lateral load test are presented in Table 1.
Since it is difficult to prepare a new clayey soil layer consistent with the previous condition, lateral load tests and consolidation tests were separately performed by installing breakwaters of various dimensions in the individual soil ground. The various conditions of breakwater sections for lateral load tests and consolidation tests are presented in Tables 2 and 3, respectively. In the model tests to investigate lateral behavior, the incremental dead load was applied in the lateral direction to the breakwater (Fig. 5a). The lateral displacement was measured for each loading step. In the model tests to examine consolidation behavior, the dead loads were applied to the top of each breakwater at every loading step (Fig. 5b). The consolidation settlement for each breakwater was obtained with time by using 0.3 m rulers, which were attached to both sides of the breakwater. The next loading step was carried out only after no additional settlement occurred. 4.2. Numerical simulations Numerical analyses were conducted to investigate the effects of various factors, such as thickness of the clayey layer, embedded depth, buoyant box as well as base width and bottom wall length, on the lateral and consolidation behaviors of a soft-ground breakwater. A general-purpose finite element program ABAQUS (Anonymous, 1998) was employed alongwith consideration of the real soil and structural conditions. The analysis of the breakwater was treated as a two-dimensional plane strain problem. Eightnoded quadrilateral elements were chosen, and nine Gaussian points were used for the construction of the stiffness matrices. Fig. 6 shows the typical finite element mesh used in this study. The number of nodes and elements were 1749 and 587, respectively. The widths and heights of soil layers were 12H (H: the height from surface to top of the breakwater) and 2.6H, respectively. Thus, the effect of the outer boundary could be neglected. The boundary
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Table 1 Soil properties of kaolinite used in this test Soil properties
Specific gravity (Gs)
Unit weight (g, kg/m3)
Initial void ratio (e0)
Liquid limit (LL)
Plastic limit (PL)
Compression index (Cc)
Swelling index (Cs)
Value
2.61
1670
1.21
46.3
22.0
0.275
0.027
Table 2 Summary of lateral model test program
Base width (Bl, m) Bottom wall length (Dl, m)
LT-1
LT-2
LT-3
LT-4
LT-5
LT-6
LT-7
LT-8
LT-9
0.1 0
0.1 0.05
0.1 0.1
0.1 0.15
0.2 0
0.2 0.05
0.2 0.1
0.2 0.15
0.4 0
Note: Embedded depth (De,l) and height from the ground surface to the top of breakwater (Hl) is 0.025 m and 0.05 m for all types, respectively.
Table 3 Summary of consolidation model test program
Base width (Bc, m) Bottom wall length (Dc, m)
CT-1
CT-2
CT-3
CT-4
CT-5
CT-6
0.12 0.035
0.16 0
0.16 0.035
0.16 0.055
0.16 0.075
0.2 0.035
Note: Embedded depth (De,c) and height from the ground surface to the top of breakwater (Hc) are 0 m and 0.08 m for all types, respectively.
condition for displacement is specified as shown in Fig. 6, and initial static pore water pressures were applied at the soil elements by considering the water depth of 6 m. Throughout this paper, a volumetric work-hardening soil model, the modified cam clay (MCC) model, was used. The MCC model is based on the critical state concepts (Schofield and Wroth, 1968) and is capable of predicting quantitatively many of the observed features of normally consolidated and lightly overconsolidated clays, and has been used in predicting real boundary value problems. The consolidation analysis was conducted by deploying Biot’s (1941) coupled consolidation theory. The breakwater was modeled as concrete beam elements, and a negative body force was applied for elements as buoyant force. Various conditions applied in the numerical simulations are presented in Table 4. For convenience, the dimensions of the breakwater were normalized by H. Table 5 shows the soil conditions used as input values in this analysis; they were classified into three types with respect to the consolidation characteristics: very soft clays (case I), soft clays (case II), and medium clays (case III). The values are based on the real soil conditions of the sites where port D is scheduled to be located in Korea (Park et al., 2002). For cases I and III in Table 5, the values of the other parameters including e0 were assumed to be the same as those of case II except l and k, which were varied only to determine the effect of the consolidation parameters on the consolidation behavior of the breakwater. For the simulation of lateral loading, the lateral displacement at the top of the breakwater was checked while the wave force was applied to the breakwater. The
period (T) and height (Hmax) of the wave were assumed to 3.5 s and 2.0 m, respectively. For the simulation of the consolidation process, the maximum consolidation settlements at the top of the breakwater were checked at the end of the consolidation process. 5. Lateral behavior of soft-ground breakwater The effects of the various factors such as dimensions of the structures and soil ground conditions on the lateral behavior of the breakwaters were investigated by model tests and numerical simulations. Fig. 7 shows the typical load-displacement curves for various conditions of breakwater, which were obtained from lateral model tests. The displacement was measured at a point 0.01 m below from the top of the breakwater. Test results in this study showed that regardless of the base width, the overturning failure mode was generally dominant over that of sliding, which may be due to the effect of breakwater embedment to the ground with values of 0.5Hl ( ¼ 0.025 m, Hl: the height from surface to the top of the breakwater in lateral model test), as indicated in Table 2. The effect of the embedded depth on the lateral behavior could be verified in Fig. 8, which compares the lateral displacements at the top of the breakwater for various embedded depths and thicknesses of the clayey layer. Unlike the model test results, numerical results in Fig. 8 were plotted in terms of the lateral displacement, which is also an important variable in designing breakwaters and is comparable to the maximum lateral resistance representing the maximum load corresponding to 0.0015 m of lateral displacement, as shown in
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I.S. Jang et al. / Ocean Engineering 34 (2007) 2240–2250 Table 4 Summary of numerical simulations Base width (B) Bottom wall length (D) Embedded depth (De) Thickness of soil layer (H’) Thickness of buoyant box (Hb)
1.5H, 2.0H, 2.5H, 3.0H, 3.75H 0H, 0.25H, 0.5H, 1.0H 0.0 m, 1.0 m, 2.0 m, 3.0m 1.0H, 1.5H, 2.0H, 2.5H, 3.0H 0.0 m, 0.25 m, 0.5 m, 0.75 m, 1.0 m
Note: The values in bold correspond to the elementary case in the parametric study.
Table 5 Input parameters used in finite element analysis Input parameters
g (kg/m3)
e0
l
k
f (1)
M
n0
K0
Case I Case II Case III
1500 1500 1500
1.0 1.0 1.0
0.52 0.37 0.13
0.058 0.040 0.002
25.4 25.4 25.4
1.0 1.0 1.0
0.3 0.3 0.3
0.5 0.5 0.5
Symbols) g : unit weight, e0 : initial void ratio, l(¼ Cc/2.3; Cc: compression index), k(¼ Cs/2.3; Ce: swelling index), f : internal friction angle, M : slope of critical state line, n0 : drained poisson’s ratio, K0 : earth pressure coefficient at rest.
Fig. 5. Basic concept of model test: (a) lateral test; and (b) consolidation test.
Fig. 7. Load–displacement curves for various breakwater sections (from model tests).
Fig. 6. Finite element mesh.
Fig. 7. Fig. 8 also reveals that the lateral displacement increases with increasing thickness of the clay layer, but is constant for a thickness higher than 2.0H. This means that
the soft-ground breakwater could be more effectively utilized for a site with a very thick clay layer than for conventional breakwaters. The effects of base widths and bottom wall lengths of soft-ground breakwaters on lateral behavior are shown in
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Fig. 9, which presents both the results of numerical simulations (Fig. 9a) and model tests (Fig. 9b). Both results reveal that the lateral displacement apparently decreases with the increase in base width and that the installation of the bottom wall has an effect on the lateral resistance as much as the increase in the base width. It is predicted that as the bottom wall length increases, the passive earth pressure force (Fp) acting on both sides of the bottom wall plays a great role in the resistance against overturning failure, rather than on the cohesion force (Fc) and on the vertical reaction force of the ground (FR). Therefore, if it is difficult to increase the base width because of economical and/or constructional problems, the lateral resistance can be successfully activated by installing the bottom wall.
Fig. 8. Comparison of lateral behavior for various embedded depths and thicknesses of clay layers (from numerical results).
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6. Consolidation behavior of soft-ground breakwater 6.1. Consolidation settlement with time and loads Consolidation model test results are shown in Fig. 10, which plot the load–settlement curves with time with respect to the base width and the bottom wall length. The curves are similar to the typical time-settlement curve measured at the base of embankment constructed on soft ground (Brugger et al., 1998). The consolidation settlements apparently increase with time as the bottom wall length and base width decreases. Fig. 11a shows the settlement due to applied loads in logarithm scale, for all fix types in the model test. The values at which no further increment occurred were plotted. The curves show that the abrupt settlements occurred at the second step (load ¼ 155.2 N) of CT-1, CT-2 and CT-3. For CT-1, the test was terminated because of the excessive punching shear failure in the second step of the consolidation process. The steep slopes in settlements may be related to the maximum past pressure, as also generally indicated by the conventional oedometer test results. However, it can be suggested that the steep slopes in this study are attributed to the effect of the instantaneous settlement due to applied load rather than the effect of the maximum past pressure because the kaolinite consolidated in slurry state, and the pressure due to mortar blocks as initial loads, which were applied at the ground surface prior to consolidation test, was less than 5 kPa. Instantaneous settlement generally means an elastic settlement. In this test, however, the elastic settlement calculated was less than 0.001 m, which can be negligible compared with total settlement. The results indicate that the settlement occurred in a plastic state rather than an elastic state, that is, at punching shear failure, which could be seen in a shallow foundation constructed on loose sands or sensitive clays. Therefore, the punching shear failure should be considered in the evaluation of the consolidation behaviors of the soft-ground breakwater.
Fig. 9. Comparison of lateral behavior for various base widths and bottom wall lengths: (a) numerical results; and (b) model test results.
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Fig. 10. Load–settlement curves with time (from model tests): (a) Loadsettlement curves for various base widths; (b) Load–settlement curves for various bottom wall lengths.
It is difficult to determine the pure consolidation settlement from the total settlement because instantaneous settlement due to the punching shearpffiffifailure cannot be obtained rigorously. In this study, the t method, which is one of the methods to estimate the coefficient of consolidation (cv) from a consolidation curve with time in a conventional oedometer test, was alternatively used to separate the instantaneous settlement from the total settlement. Fig. 12pshows the consolidation curve with ffiffi time plotted in the t axis, where the initial instantaneous settlement can be graphically evaluated by finding out the start time of consolidation (t0) from the initial tangential pffiffi line. The load–settlement curves modified by using the t method are shown in Fig. 11b.
Fig. 11. Settlements due to applied loads in logarithm scale for all six types: (a) original load–settlement curves; (b) modified load–settlement curves.
6.2. Parametric analysis on the consolidation settlement of the breakwater Consolidation settlement of the soft-ground breakwater is mainly influenced by the stress increment generated at soil mass due to self-weight of the breakwater. The effect of the stress increment was investigated by modeling numerically the consolidation of a soft-ground breakwater without a bottom wall. The variation of the vertical stress increment with depth was checked at the elements corresponding to the center of the base of the breakwater, which is plotted in Fig. 13. The stress increment decreases with the distance from the base, to be zero at about 20 m,
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Fig. 12. Consolidation curve with time plotted by the
pffiffi t method.
Fig. 13. Variation of the vertical stress increment with depth.
which is almost the same as a base width (B). The numerical results are somewhat different to the elastic solution of Boussinesq (1885), which shows 10% of the total load is transmitted up to the depth of 2B. This may be attributed to the fact that the stress increment at a soft soil
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with a plastic behavior is less than that of an elastic soil. This is why the stress increment for case III representing the relatively stiffer soil layer is transmitted to a higher depth than that for case I. It can also be predicted that the consolidation of the breakwater converges to a constant value if the thickness of the clayey layer is greater than twice the height of the breakwater. This is verified from Fig. 14a, which plots the maximum consolidation settlement with the thickness of the clay layer and the embedded depth. Numerical results in Fig. 14a also reveal that the consolidation settlement decreases as the embedded depth increases. This is because the adhesion of the clayey soils with a stem embedded into the ground contributes to restrain the consolidation settlement. One of the important features of the soft-ground breakwater is the buoyant box, which is utilized to reduce the self-weight of the breakwater. Finite element analyses were performed to examine the effect of the buoyant box on the consolidation settlement of the breakwater. As shown in Fig. 14b, which plots the maximum consolidation settlement with the thickness of the buoyant box for case II, the size of the buoyant box is linearly correlated to the consolidation settlement. As the thickness of the buoyant box increases, both the self-weight of the breakwater and the consolidation settlement decrease. The results indicate that the settlement can be effectively controlled with the buoyant box even for a very soft clay layer, where excessive settlement is predicted in a practical design. As the base width of the breakwater increases, the self-weight of the breakwater increases, but the stress increment decreases. Fig. 14c shows the numerical results of the maximum consolidation settlements with the base width (B) and the bottom wall length (D) of the breakwater for a ground condition of case II. The results for all cases show that the consolidation settlement decreases with increases in base width and bottom wall length. For a breakwater with a high bottom wall (D ¼ 1.0H), consolidation settlement is retarded by the bottom wall and not by the decrease in the stress increment, because the longer the bottom wall length the more a mobilized area to resist the settlement. In this case, the effect of the base width is of secondary importance. The settlement tendencies are almost the same, regardless of ground conditions. The model test results of the consolidation settlement with the base width and the bottom wall length are shown in Fig. 15. The results are modified in consideration of the pffiffi instantaneous settlement obtained by the t method, as mentioned above. The trend in the consolidation settlement with the bottom wall length and the base width is similar to the numerical results. From the numerical and model test results, it is suggested that the increase in the bottom wall length is more effective than the increase in the base width to reduce the consolidation settlement as well as the lateral resistance, if the economical design efficiency is considered.
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Fig. 15. Maximum consolidation settlements with the base width and the bottom wall length (model test results): (a) effect of the base width; and (b) effect of the bottom wall length.
7. Application of the Terzaghi’s one-dimensional consolidation theory
Fig. 14. Maximum consolidation settlements for various conditions (numerical results): (a) effect of embedded depth and thickness of clay layers; (b) effect of buoyant box; and (c) effect of base width and bottom wall length.
The consolidation settlements of the conventional breakwater have been generally computed by the Terzaghi’s 1-D consolidation theory. However, the soft-ground breakwater has a complex bottom wall system, so the theory cannot be applied directly. For convenience in practical design, the applicability of the Terzaghi’s theory to the soft-ground breakwater was examined by comparing the consolidation settlements obtained from numerical simulations and model tests with the computed values from the Terzaghi’s theory. The consolidation settlements of a breakwater without the bottom wall were obtained from numerical analysis and compared with theoretical values calculated with the stress increment at the mid-depth of single layer, as shown in Fig. 16, which reveals higher theoretical settlements than
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Fig. 16. Comparison of the settlements from the Terzaghi’s theory with FEM results.
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stress increments, which were checked at both the center and the edge of the base. The theoretical consolidation settlements modified by Skempton and Bjerrum (1957) were similar to the numerical results, which were between the values recalculated at the center and the edge. For a breakwater with a bottom wall, since the stress increment due to self-weight of the breakwater concentrates at the bottom wall, it is difficult to rigorously define the consolidation layer. Furthermore, the consolidation behavior may vary because of the increase in the resistance due to the installation of the bottom wall. To identify the relevant loading point in the application of the 1-D consolidation theory to the soft-ground breakwater, the numerical settlements were compared with the calculated ones, whose loading points were located at the tip of the bottom wall and the base, respectively (Fig. 18a). The 1-D consolidation settlements calculated under assumption that the load is applied to the soil at the tip were more similar to the numerical results than to the settlements obtained under the assumption that the base is the loading point. A similar trend can be verified from the model test results in Fig. 18b, which plots the comparison of the consolidation settlements from the model test with the calculated values. Fig. 18 indicates that the proposed evaluation method on the consolidation settlement of the soft-ground breakwater, based on the assumption of the tip of bottom wall as the loading point, can be used rather conservatively and easily with some accuracy. 8. Conclusions
Fig. 17. Comparison of the modified settlements with FEM results for case II.
the numerical settlements. The difference is caused by the fact that the numerical values are obtained under assumption of a 2-D plane strain condition and the plastic yield criterion, while the theoretical ones are calculated based on the 1-D elastic theory. To consider the 2-D effect, the consolidation settlement based on the Terzaghi’s theory was modified by using Eq. (2) of Skempton and Bjerrum (1957), as shown in Fig. 17. The correction factor, m ¼ 0.9 was obtained by assuming pore pressure parameter, A ¼ 0.75, which corresponds to normally consolidated clays. The effect of the stress increment was additionally investigated, as shown in Fig. 17, by recalculating the 1-D consolidation settlements using the numerical results of the
The authors developed a new seabed type of breakwater applicable to very soft ground, which is expected to satisfy two requirements: the prevention of excessive consolidation settlement due to the self-weight of the structure, and the assurance of sufficient lateral resistance against wave actions. From the results of model tests and numerical simulations performed to investigate the lateral and consolidation behaviors of the soft-ground breakwater, the following conclusions can be drawn. The soft-ground breakwater proposed herein can be used with high economic efficiency owing to its resistance mechanism, at a site with even a very thick clay layer. The base width and bottom wall length are mainly to do with lateral resistance, and if the base width is difficult to increase because of economical and/or constructional problems, the lateral resistance could be successfully assured by installing bottom walls. The consolidation settlement could be effectively controlled with the buoyant box even for a very soft clay layer, where excessive settlement is predicted in a practical design. The bottom wall can reduce the consolidation settlement efficiently because it can decrease the thickness of the consolidation layer and increase the resistance. Terzaghi’s one-dimensional consolidation theory can be adopted rather conservatively with some accuracy if the location
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Fig. 18. Comparison of the measured consolidation settlements with values from Terzaghi’s 1-D theory: (a) FEM results; and (b) model test results.
of consolidation loading is assumed to be at the end of the bottom wall. Acknowledgment This research was accomplished as a part of the project ‘‘Technologies for Breakwaters in Deep Water and Soft Ground Improvement’’, which was sponsored by Ministry of Maritime and Fishery in Korea. The authors express their appreciation for this support. References Anonymous, 1998. ABAQUS/Standard User’s Manual—Version 5.8. Hibbit, Kalsson and Sorenssen Inc. Biot, M.A., 1941. General theory of three-dimensional consolidation. Journal of Applied Physics 12, 155–164. Boussinesq, J., 1885. Application des Potentials a L’Etude de L’Equilibre et du Mouvement des Solides Elastiques. Gauthier-Villars, Paris. Brugger, P.J., Almeida, M.S.S., Sandroni, S.S., Lacerda, W.A., 1998. Numerical analysis of the breakwater construction of Segipe Harbour, Brazil. Canadian Geotechnical Journal 35, 1018–1031. Cho, I.H., Kim, M.H., 1998. Interactions of a horizontal flexible membrane with oblique waves. Journal of Fluid Mechanics 367, 139–161.
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